Feyenoord fans clashed with police before their 1-1 Europa League draw with Roma in the Italian capital.
Italian police claim to have made 22 arrests and charged eight fans after trouble flared in the city centre.
Supporters damaged buildings and clashed with riot police at the Spanish Steps and left the square's Baroque fountain full of empty beer bottles.
"Feyenoord should pay for the damage caused by fans to the city," said Rome government official Livio Ricciardelli.
"They should make a public apology."
Around 7,000 Feyenoord fans are believed to have travelled to Italy for the first leg of their last-32 knockout tie at the Stadio Olimpico.
Gervinho put Roma ahead midway through the first half before Kazim Kazim-Richards equalised 10 minutes after half-time for the Dutch side.